LCM of 12, 15, 20 and 27 is 540. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. The article LCM of Two Numbers provides detailed explanations structured by expert teachers to make the learning of the LCM concept more interesting among students. Students can use this article as a reference while solving problems to enhance their learning process. Let us learn how to determine the least common multiple of 12, 15, 20 and 27 with a complete explanation in this article.
What is LCM of 12, 15, 20 and 27?
The answer to this question is 540.
How to Find LCM of 12, 15, 20 and 27?
LCM of 12, 15, 20 and 27 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15, 20 and 27 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. Hence the numbers 12, 15, 20 and 27 are written as;
12 = 2 × 2 × 4
15 = 3 × 5
20 = 2 × 2 × 5
27 = 3 × 3 × 3
LCM (12, 15, 20, 27) = 2 × 2 × 3 × 3 × 3 × 5 = 540
LCM of 12, 15, 20 and 27 Using Division Method
In this method, to find the LCM of 12, 15, 20 and 27, we divide the numbers 12, 15, 20 and 27 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 12, 15, 20 and 27.
| 2 | 12 | 15 | 20 | 27 |
| 2 | 6 | 15 | 10 | 27 |
| 3 | 3 | 15 | 5 | 27 |
| 3 | 1 | 5 | 5 | 9 |
| 3 | 1 | 5 | 5 | 3 |
| 5 | 1 | 5 | 5 | 1 |
| x | 1 | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (12, 15, 20, 27) = 2 × 2 × 3 × 3 × 3 × 5 = 540
LCM of 12, 15, 20 and 27 Using Listing the Multiples
In this method, the multiples of each number are listed until the first common multiple is found. Few multiples of 12, 15, 20 and 27 are as follows:
Multiples of 12 : 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………, 516, 528, 540, ….…
Multiples of 15 : 15, 30, 45, 60, 75, 90, 105, 120,135, 150,…….., 510, 525, 540, ……
Multiples of 20 : 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ……, 500, 520, 540, ….….
Multiples of 27 : 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, ……, 486, 513, 540, ……
LCM (12, 15, 20, 27) = 540
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by 12, 15, 20, 27 exactly?
Solution: 540 is the smallest number that is divisible by 12, 15, 20, 27 exactly.
Q. 2: Which of the following is the LCM of 12, 15, 20 and 27?
540, 120, 27, 52
Solution: The LCM of 12, 15, 20 and 27 is 540.
Frequently Asked Questions on LCM of 12, 15, 20 and 27
What is the LCM of 12, 15, 20 and 27?
What are the methods used to find the LCM of 12, 15, 20 and 27?
The following methods are used to find the LCM of 12, 15, 20 and 27
Prime Factorisation
Division Method
Listing the Multiples
540 is the LCM of 12, 15, 20 and 27. True or False.
Using the prime factorisation method, find the LCM of 12, 15, 20 and 27.
Here, we express the numbers as the product of prime factors
12 = 2 × 2 × 4
15 = 3 × 5
20 = 2 × 2 × 5
27 = 3 × 3 × 3
LCM (12, 15, 20, 27) = 2 × 2 × 3 × 3 × 3 × 5 = 540
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